Coulombic interactions energy components

For the details and derivation of the physical interpretation we refer the reader to the original literature14,15. Since the Coulomb self-energy component of the KS electron-interaction energy functional and its derivative, the Hartree potential, are known functionals of the density, we provide in Section HA the expressions governing the interpretation of the KS exchange-correlation energy... 

We also focused [156] on the Coulomb energy between atoms in supermolecules. We proposed an atom-atom partitioning of the Coulomb interaction, which should not be confused with the electrostatic component of the intermolecular interaction, defined within the perturbation approach. Instead, this atom-atom Coulomb interaction energy uses the total molecular (in the case of a single, covalently boimd molecule) or the supermolecular (in... 

Table 13-8. Self-interaction error components for Coulomb and exchange energies (Ej + Ex) as well as for the correlation energy (Ec), and the resulting sum for the H atom, the H2 molecule, and the H3 transition structure [kcal/mol]. Data taken from Csonka and Johnson, 1998.

An additional electrostatic component to the polymer interaction term is typically unimportant since the counterions strongly screen any Coulomb interactions [92]. Finally, an electrostatic interaction between polymers and counterions Tint occurs if the PE brush is not locally electro-neutral throughout the system, an example is depicted in Fig. 10a. This energy is given by... 

Exchange Energy. An attractive (negative) component of the electron-electron interaction energy. Arises due to an overestimation of the repulsive (positive) component or Coulomb energy. 

Continuum models are the most efficient way to include condensed-phase effects into quantum-mechanical calculations, and this is typically accomplished by using the self-consistent reaction field (SCRF) approach for the electrostatic component. Therefore it is very common to replace the quantal problem by a classical one in which the electronic energy plus the coulombic interactions of the nuclei, taken together, are modeled by a classical force field—this approach usually called molecular mechanics (MM) (Cramer and Truhlar, 1996). 

The Hamiltonian is the total energy operator for a system, and is written as the sum of the kinetic energy of all the components of the system and the internal potential energy. In an atom or molecule, comprised of positive nuclei and negative electrons, the potential energy is simply that due to the coulombic interactions present. Thus for the kinetic energy in a system of M nuclei and N electrons ... 

Fint is the free energy of non-Coulomb interactions of monomer units. Finl can be expressed, for example, in terms of the Flory-Huggins lattice theory [21]. In the general case, when network is immersed in solvent which includes 1 different components some of which can be polymeric with the degree of polymerization Pi(Pi 1, i = L 2,... k), Fim in the Flory-Huggins theory has the following form [21-22] ... 

Here e(fe) and V(k) are Fourier components of the hopping t j and the hybridization T. All energies in (6) are counted from p. Due to the relations (4) the problem of calculation of all electron GFs reduces to the calculation of d-electron GF with strong Coulomb interaction. 

Fig. S a Valence band spectra of Gd C82 (grey) and C82 (black) measured with Al Ka x-rays, b Symbols Gd 4f photoemission after subtraction of the empty C82 C 2s/2p spectrum. The vertical lines are individual components of atomic calculations for a 4f> multiplet, and the solid curve is their broadened sum. c Gd-N4>5 x-ray absorption spectrum (Gd 4d-4f excitations) of Gd C82. The complex lineshape comes from the widely spaced multiplet components resulting from the strong Coulomb interaction between the single hole in the 4d shell and the eight electrons present in the 4f shell in the x-ray absorption final state [see Fig. lc]. The arrows represent the two photon energies used for the data shown in panel d. d Resonant photoemission data of the valence band region of Gd C82 recorded off (hv=137 eV) and on (hv=149 eV) the Gd 4d-4f giant resonance...

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